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Simplifying x2 + 78x = 729 Reorder the terms: 78x + x2 = 729 Solving 78x + x2 = 729 Solving for variable 'x'. Reorder the terms: -729 + 78x + x2 = 729 + -729 Combine like terms: 729 + -729 = 0 -729 + 78x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + 78x + 729 + x2 = 0 + 729 Reorder the terms: -729 + 729 + 78x + x2 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + 78x + x2 = 0 + 729 78x + x2 = 0 + 729 Combine like terms: 0 + 729 = 729 78x + x2 = 729 The x term is 78x. Take half its coefficient (39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. 78x + 1521 + x2 = 729 + 1521 Reorder the terms: 1521 + 78x + x2 = 729 + 1521 Combine like terms: 729 + 1521 = 2250 1521 + 78x + x2 = 2250 Factor a perfect square on the left side: (x + 39)(x + 39) = 2250 Calculate the square root of the right side: 47.434164903 Break this problem into two subproblems by setting (x + 39) equal to 47.434164903 and -47.434164903.Subproblem 1
x + 39 = 47.434164903 Simplifying x + 39 = 47.434164903 Reorder the terms: 39 + x = 47.434164903 Solving 39 + x = 47.434164903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = 47.434164903 + -39 Combine like terms: 39 + -39 = 0 0 + x = 47.434164903 + -39 x = 47.434164903 + -39 Combine like terms: 47.434164903 + -39 = 8.434164903 x = 8.434164903 Simplifying x = 8.434164903Subproblem 2
x + 39 = -47.434164903 Simplifying x + 39 = -47.434164903 Reorder the terms: 39 + x = -47.434164903 Solving 39 + x = -47.434164903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = -47.434164903 + -39 Combine like terms: 39 + -39 = 0 0 + x = -47.434164903 + -39 x = -47.434164903 + -39 Combine like terms: -47.434164903 + -39 = -86.434164903 x = -86.434164903 Simplifying x = -86.434164903Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.434164903, -86.434164903}
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